Non-negativity of GM^{(3)} for general tripartite quantum states

Determine whether the genuine multi-entropy GM^{(3)}(A:B:C) = S^{(3)}(A:B:C) − 1/2 [S(A) + S(B) + S(C)] is non-negative for all pure tripartite quantum states, beyond the class of time-symmetric holographic states where non-negativity is established.

Background

The paper compares two signals of tripartite entanglement in pure three-party states: the residual information R^{(3)}(A:B) and the genuine multi-entropy GM^{(3)}(A:B:C). Both signals vanish for states with only bipartite entanglement. R^{(3)} is known to be non-negative for any quantum state, while GM^{(3)} is defined via the multi-entropy S^{(3)} and subtracting half the sum of single-party entropies.

Within holography, GM^{(3)} has been shown to be non-negative in time-symmetric spacetimes. However, the authors point out that outside holography, the general non-negativity property of GM^{(3)} has not been established, leaving open whether GM^{(3)} can ever be negative for general quantum states or whether a universal non-negativity theorem holds.